The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  2  0  2  2 2a+2 2a+2 2a+2 2a+2 2a+2 2a+2  0  0  2  2 2a  0  2
 0  0  2  0 2a+2  2 2a+2  0 2a+2 2a+2  2  2 2a+2  2  0  2 2a+2  0 2a+2 2a  2
 0  0  0  2  2  2 2a 2a+2  0  2  0  2 2a 2a 2a 2a+2  0 2a 2a 2a  0

generates a code of length 21 over GR(16,4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+69x^56+54x^60+768x^63+66x^64+30x^68+15x^72+6x^76+9x^80+6x^84

The gray image is a code over GF(4) with n=84, k=5 and d=56.
This code was found by Heurico 1.16 in 0 seconds.